US11082061B2 - High-rate long LDPC codes - Google Patents

High-rate long LDPC codes Download PDF

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US11082061B2
US11082061B2 US16/559,027 US201916559027A US11082061B2 US 11082061 B2 US11082061 B2 US 11082061B2 US 201916559027 A US201916559027 A US 201916559027A US 11082061 B2 US11082061 B2 US 11082061B2
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matrix
ldpc
rate
parity check
codeword
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US20190393890A1 (en
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Guido Montorsi
Sergio Benedetto
Yan Xin
Min Yan
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Huawei Technologies Co Ltd
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    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148Structural properties of the code parity-check or generator matrix
    • H03M13/116Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105Decoding
    • H03M13/1131Scheduling of bit node or check node processing
    • H03M13/114Shuffled, staggered, layered or turbo decoding schedules
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148Structural properties of the code parity-check or generator matrix
    • H03M13/1157Low-density generator matrices [LDGM]
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148Structural properties of the code parity-check or generator matrix
    • H03M13/1174Parity-check or generator matrices built from sub-matrices representing known block codes such as, e.g. Hamming codes, e.g. generalized LDPC codes
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13Linear codes
    • H03M13/15Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
    • H03M13/151Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
    • H03M13/1575Direct decoding, e.g. by a direct determination of the error locator polynomial from syndromes and subsequent analysis or by matrix operations involving syndromes, e.g. for codes with a small minimum Hamming distance
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/61Aspects and characteristics of methods and arrangements for error correction or error detection, not provided for otherwise
    • H03M13/615Use of computational or mathematical techniques
    • H03M13/616Matrix operations, especially for generator matrices or check matrices, e.g. column or row permutations
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/65Purpose and implementation aspects
    • H03M13/6508Flexibility, adaptability, parametrability and configurability of the implementation
    • H03M13/6516Support of multiple code parameters, e.g. generalized Reed-Solomon decoder for a variety of generator polynomials or Galois fields
    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/65Purpose and implementation aspects
    • H03M13/6522Intended application, e.g. transmission or communication standard
    • H03M13/6527IEEE 802.11 [WLAN]
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/004Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056Systems characterized by the type of code used
    • H04L1/0061Error detection codes
    • H04L1/0063Single parity check

Definitions

  • An LDPC encoder at a transmitter is used for encoding source words to generate codewords.
  • An LDPC decoder at a receiver is used for decoding the received codewords.
  • LDPC codes of various rates have been adopted in the IEEE 802.11ad standard and are currently proposed in respect of the developing IEEE 802.11ay standard.
  • the long LDPC codes proposed for the 7/8 LDPC code rate have a different codeword length from than the codeword lengths used for different code rates for long LDPC codes.
  • the use of different LDPC codeword length for different code rates for long LDPC codes can impact the implementation of the blocking and de-blocking processes at the transmitter and at the receiver respectively. Accordingly, it is desirable to have a codeword length that is consistent for different code rates.
  • a new high rate, long LDPC code including a rate 7/8 (1344, 1176) LDPC code that preserves the codeword length of 1344 that is used by other LDPC codes that have different code rates, so as to simplify the implementation and increase spectrum efficiency with padding fewer zeros in encoding and single carrier (SC) blocking compared to other possible solutions.
  • H I is:
  • FIG. 4A is a diagram illustrating an example single carrier frame format of 802.11ad
  • FIG. 10 illustrates a method for generating a length 1344 LDPC matrix H I of code rate 7/8 based on rate 3/4 LDPC in 802.11 according to the present disclosure
  • FIG. 14 shows an alternative lifting matrix for use in the method of FIG. 13 ;
  • FIG. 15B is a block diagram representing an example steps in a process of decoding a received signal according to one embodiment of the present disclosure
  • the present disclosure teaches methods, devices, and systems for encoding source words and decoding codewords in a wireless network. While described below primarily with respect to 802.11ay compatible networks, the present disclosure may also be applied to other blocking coding based systems.
  • [REF 1] proposes a rate 7/8 long LDPC code generated by puncturing the first 96 parity bits of the rate 13/16 LDPC codewords of length 1344 bits.
  • the AP 104 may comprise a base station (BS), evolved Node B (eNB), wireless router, or other network interface, which functions as a wireless transmission and/or reception point for STA 102 in the network 100 .
  • the AP 104 is connected to a backhaul network 110 which enables data to be exchanged between the AP 104 and other remote networks, nodes, APs, and devices (not shown).
  • the AP 104 may support communications with each STA 102 by establishing uplink and downlink communications channels with each STA 102 , as represented by the arrows in FIG. 1A . Communications in the network 100 may be unscheduled, scheduled by the AP 104 or by a scheduling or management entity (not shown) in the network 100 , or a mix of scheduled and unscheduled communications.
  • FIG. 1B illustrates an example processing system 150 , which may be used to implement methods and systems described herein, such as the STA 102 or the AP 104 .
  • the processing system 150 may be a base station, a wireless router, a mobile device, for example, or any suitable processing system.
  • Other processing systems suitable for implementing the present disclosure may be used, which may include components different from those discussed below.
  • FIG. 1B shows a single instance of each component, there may be multiple instances of each component in the processing system 150 .
  • P 1 is obtained by shifting the columns of P o to the right by one element
  • P 3 is obtained by shifting the columns of P o to the right by three elements.
  • the identity matrix P o includes Z “1”s arranged diagonally across the matrix, with all other values being “0”.
  • any non-zero value i submatrices P i in FIGS. 5B-5D can also be obtained from the respective identity matrix P o .
  • the blank entries represent Z ⁇ Z submatrices with all zero entries.
  • the lifting matrix 602 has the same number of rows and columns (3 ⁇ 16) as the rate 13/16 matrix 604 of 802.11ad.
  • Each cell element in the lifting matrix 602 is assigned one of the three possible values “1”, “0”, and “ ⁇ 1”. If a submatrix of the base matrix 604 is null (i.e. all zero entries), which is denoted as “4”, the corresponding entry in the lifting matrix 604 is also denoted as “ ⁇ 1”.
  • the entry at row 1, column 16 of the lifting matrix 604 corresponds to the submatrix at row 1, column 16 of the base matrix 602 .
  • Both the entry of the lifting matrix 604 and the submatrix of the base matrix 602 have the value of “ ⁇ 1”.
  • the corresponding entries of the lifting matrix 602 also have the value of “ ⁇ 1”. Applying the one entry with the value of “ ⁇ 1” in the lifting matrix 602 to the corresponding submatrix in the base matrix 604 generates four null submatrices.
  • the IEEE 802.11ad standard specifies an LDPC code with a high code rate of 7/8 (REF 2).
  • [REF 1] has proposed a rate 7/8 LDPC code with codeword length of 1248.
  • the rate 7/8, length 1248 LDPC code [REF 1] is generated by puncturing the first 96 parity bits from the rate 13/16 (1344, 1092) LDPC code represented by the matrix 606 shown in FIG. 6A , which as indicated above is derived from the rate 13/16 length 672 base LDPC code specified in 802.11ad.
  • a transmitter does not transmit the punctured bits, and the receiver puts equal likelihood for 1/0 for the punctured bits.
  • the proposed rate 7/8 LDPC code of FIG. 6A that is generated through puncturing results in a codeword length of 1248 rather than the codeword length of 1344 proposed for the long code, lower rate LDPC codes.
  • Every three SC data blocks (BLK 1 , BLK 2 , BLK 3 ), which each contain 448 symbols, are constructed from 2 symbol codewords (each block is constructed from 1 or 2 codewords).
  • QPSK QPSK
  • a 1248 bit codeword after modulation becomes a 624 symbol codeword.
  • the blocking process becomes more complex: every 39 data blocks are constructed from 28 codewords, and each data block is constructed from one or two codewords.
  • FIG. 7C shows examples of SC 64QAM blocking with (1344, 1176) LDPC (left side) as compared to (1248, 1092) LDPC (right side).
  • (1344, 1176) LDPC with 64QAM, one 1344 bit codeword after modulation becomes one 224 symbol codeword. Each 448 symbols data block is constructed from two 224 symbol codewords.
  • (1248, 1092) LDPC one 1248 bit codeword after modulation becomes one 208 symbol codeword.
  • the blocking process becomes more complex: every 13 data blocks are constructed from 28 codewords, and each data block is constructed from 3 or 4 codewords.
  • the rate 7/8 length 672 LPDC matrix Hn 860 in [REF 2] is derived by summing rows from the 802.11ad specified rate 3/4 length 672 (672, 504) LDPC matrix H 850 .
  • the sub-matrices from the first row R 1 and third row R 3 of base code matrix H 850 are summed to provide sub-matrices for corresponding column entries in the first row of new LDPC matrix Hn 850
  • the sub-matrices from the second row R 2 and the fourth row R 4 of base code matrix H 850 are summed using modulo-2 addition to provide sub-matrices for corresponding column entries in the second row of new LDPC matrix Hn 850 .
  • the 802.11ad specified rate 3/4 length 672 (672, 504) LDPC matrix H 850 is once again used as a base matrix, however, instead of using an extended lifting factor as discussed in the immediately preceding example, a lifting matrix 1110 is used to generate an intermediate matrix H int 1120 .
  • the lifting matrix 1110 is selected through an optimization search using criteria to yield an optimized error rate performance. In the illustrated embodiment lifting matrix 1110 is selected such that it first and third rows are complementary and its second and fourth rows are complementary.
  • the sub-matrices from the first row R 1 and fifth row R 5 of intermediate matrix H int 1120 are summed using modulo-2 addition to provide sub-matrices for corresponding column entries in the first row of new LDPC matrix H I 1130 .
  • FIG. 14 shows an example of a further optimized lifting matrix 1410 that may be used in some examples in place of lifting matrix 1310 .
  • a regular row-column interleaver is included between encoding at LDPC encoder and modulating at Bit-to-Symbol modulator 206 .
  • An LDPC encoded signal may be received at a receiver of the STA 102 or AP 104 .
  • the receiver includes an equalization and de-blocking module 1502 , a demodulator 180 , an LLR calculator 1506 , and an LDPC decoder 190 .
  • the LLR calculator 1506 can be a component of the demodulator 180 .
  • the equalization and de-blocking module 1502 first equalizes the received signal 1501 to reduce intersymbol interference caused by the channel through which the received signal is transmitted, and then de-blocks the equalized signal to recover the codewords symbols (step 1522 ).
  • FIG. 16 is an example LDPC decoder using message passing algorithm to decode the LDPC encoded source words.
  • Other decoding algorithm may also be used to implement the LDPC decoding.
  • the LDPC decoder 190 may include a controller 1602 , a check nodes module 1604 and a variable node module 1606 .
  • H n comprises a plurality of submatrices, and each submatrix has a size of Z ⁇ Z. The methods of generating the parity check matrix have been described in the encoding process.
  • each variable node 1704 sends a message (“extrinsic information”) to each check node 1702 to which the variable node 1704 is connected.
  • Each check node 1702 sends a message (“extrinsic information”) to variable nodes 1704 to which the check node 1702 is connected.
  • “Extrinsic” in this context means that the information the check nodes 1702 or variable nodes 1704 already possess is not passed to that node.
  • the cyclic shift structure simplifies the decoder architecture that allows to feed the parallel processors with a simple barrel shifter.
  • the present disclosure provides certain example algorithms and calculations for implementing examples of the disclosed methods and systems. However, the present disclosure is not bound by any particular algorithm or calculation. Although the present disclosure describes methods and processes with steps in a certain order, one or more steps of the methods and processes may be omitted or altered as appropriate. One or more steps may take place in an order other than that in which they are described, as appropriate.
  • the present invention may be implemented by using hardware only, or by using software and a necessary universal hardware platform, or by a combination of hardware and software. Based on such understandings, the technical solution of the present invention may be embodied in the form of a software product.
  • the software product may be stored in a non-volatile or non-transitory storage medium, which can be a compact disk read-only memory (CD-ROM), USB flash drive, or a hard disk.
  • the software product includes a number of instructions that enable a computer device (personal computer, server, or network device) to execute the methods provided in the embodiments of the present invention.

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